C-program for finding prime factors, compilation is not stopping - c

Question

My Program to calculate the largest prime factor of 600851475143, is stuck and never stops during compilation and execution. Does anyone know why it does not finish execution?
#include <stdio.h> //Edited the #includes(typo) to #include
int main (void)
{
long long int num = 600851475143 ;
long long int factorCount;
long long int bigFactor;
for ( long long int i=1 ; i <= num; i+=2 )// Iterating through all numbers from 2, smaller than or equal to num
{
if ( num % i == 0) // If the number "i" is a factor of num i.e. If "i" perfectly divides num
{
factorCount = 0;
//checking whether a factor "i" , is a prime factor of num
for ( long long int j=2; j <= i ; j++ ) // Iterating through all numbers from 2, smaller than or equal to "i"
{
if ( i % j == 0) // If the number "j" prefectly divides or is a factor of "i"
{
factorCount++; //Add 1 to factorCount
};
};
if ( factorCount == 1 ) // If factorCount has not exceeded 1 i.e., the number "i" is a prime number
{
bigFactor = i;
};
};
};
printf("The largets prime factor of %lli is %lli\n",num,bigFactor );
return 0;
}

Answer 1

I am not sure whether I understood your question .. so you just want to get the biggest prime factor for a certain number? If this is the case, then just do the following:
#include <stdio.h>
#define NUMBER 600851475143
int main (void)
{
long long int num = NUMBER;
long long int factor;
for (factor=2 ; num != 1; factor++) {
if (num % factor == 0) {
num = num / factor;
factor = factor-1;
}
}
printf("The largets prime factor of %lli is %lli\n",NUMBER, factor);
return 0;
}
Why this works: the first prime factor you find is the smallest prime factor of the number; the last prime factor is the biggest. Therefore once you have found a prime factor p, there does not exist a prime factor smaller than p, because otherwise you would have found that smaller prime factor before. Hence your next prime factor is greater equals p.

Answer 2

It finishes its execution, it just takes a lot of time.
You are performing a loop 600851475143 / 2 times or about 300 billion times. If the main loop takes 1ms to executes (but it should take more since there is another inner loop) then it means that time required would be about 9.5 years.
Just be patient and your loop will finish.

Answer 3

Try this:
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
int main (void)
{
long long int num = 600851475143 ;
long long int factorCount;
long long int bigFactor;
for ( long long int i=1 ; i <= sqrt(num); i+=2 )// Iterating through all numbers from 2, smaller than or equal to num
{
if ( num % i == 0) // If the number "i" is a factor of num i.e. If "i" perfectly divides num
{
factorCount = 0;
//checking whether a factor "i" , is a prime factor of num
for ( long long int j=2; j <= i ; j++ ) // Iterating through all numbers from 2, smaller than or equal to "i"
{
if ( i % j == 0) // If the number "j" prefectly divides or is a factor of "i"
{
factorCount++; //Add 1 to factorCount
};
};
if ( factorCount == 1 ) // If factorCount has not exceeded 1 i.e., the number "i" is a prime number
{
bigFactor = i;
};
};
};
printf("The largets prime factor of %lli is %lli\n",num,bigFactor );
return 0;
}
Only calcule the root of 600851475143.

Answer 4

Good Afternoon 24,
The runtime of this code will take very long, very very long. But it should work, only real error is the 's' in
#includes <stdio.h>
so just be patient, you're dealing with very large numbers, iterating through odd numbers has made it much less lengthy than it could be, don
Note: If you are using an online IDE such as cpp.sh or other source, the website will most likely time out. Please use a locally installed IDE.

Answer 5

Well, my best guess would be that it runs perfectly fine but takes too much time.
So what you have to do is optimize your algorithm.
Here are some hints for improving your algorithm:
You just need to iterate until the square root of a number to know whether or not it is a prime.
As you have done in our outer loop (but not in your inner loop), you just have to iterate through odd numbers.
Since you are looking for the highest prime factor, try beginning from the end and once you have reached a prime factor, stop looking.
I think that this should run in a reasonable amount of time.
EDIT: Actually, after reflexion the third point is not that obvious. Of course, it is better than going through all factors but the computation is way slower for large factors ...

Answer 6

This is reasonably efficient:
#include <stdio.h>
#define NUMBER 600851475143
static unsigned long long int gpf(unsigned long long n)
{
unsigned long long d, q;
while (n > 2 && !(n & 1))
n >>= 1;
d = 3;
while (d * d <= n) {
q = n / d;
if (q * d == n)
n = q;
else
d += 2;
}
return n;
}
int main(void)
{
printf("The largest prime factor of %llu is %llu\n",
NUMBER, gpf(NUMBER));
return 0;
}